We Helped With This R Programming Assignment: Have A Similar One?

Exam12018

Mark F Owens

September 26, 2018

Instructions

Please start with this exam template and create a new file in R Markdown called “exam1_your_name” to answer the following questions. Please change the name of the author as well. The questions in Part 1 do not require use of R, but you can type your answers into this R Markdown file if you would like. Part 2 requires you to use R. When you are finished, please knit the file and upload it to Canvas.

Part 1 (40 Total Points)

1. Suppose you want to investigate the factors which predict a student’s grade on the econometrics exam.

(a)     Which factors that your instructor can observe do you think are important? (3 points)

(b)     Are there other important factors that your instructor cannot observe? (3 points)

2. Suppose you have daily sales data and weather reports from 2000-2018 for a restaurant. You want to determine if sales are related to the number of sunny days.

(a)     What kind of data do you have? (2 points)

(b)     Which is the dependent variable and which is the independent variable in this relationship? Briefly explain.(3 points)

3.     Specifically, what does it mean to have a coefficient with a p-value such that p<0.05? (3 points)

4.     Let colgpa denote the grade point average for a college student and let hsgpa denote the student’s gpa in high school. A simple model relating college gpa to high school gpa is

colgpa = β₀ + β₁hsgpa + µ,

in which µ represents the unobserved error.

(a)     What factors are contained in µ? (3 points)

(b)     Would you expect sign of β^ˆ₁ to be positive, negative, or zero? Explain your answer. (3 points)

(c)     What characteristics would the hsgpa variable need to have in order for this simple regression model to uncover the “ceteris paribus” causal effect of hsgpa on colgpa? Explain. (3 points)

5. You are given the following table of output pertaining to voters in a sample of urban voting districts across the country. Voters is the number of voters who cast a ballot in 100s, and TV ads is the number of political advertisements purchased for TV in the market.

Table 1: OLS regression TV advertisements and voters

Dependent variable:

(a)     Use the information in the table to write the regression equation. (3 points)

(b)     According to the results, how many voters are generated from each TV advertisement? (3 points)

(c)     How much of the variation in voters is explained by this model? Interpret this finding. (3 points)

(d)     Suppose one of the voting districts is Erie. There are 30 TV ads in Erie, and 6000 voters. Use the output in the table to calculate the predicted number of voters. (2 points)

(e)     What is the residual for Erie? (2 points)

(f)      Did Erie have more or fewer voters than would be expected for the number of TV Ads? (2 points)

(g)     What other factors would enter into the residual of this regression? (2 points)

Part 2: Data questions using R (60 Total Points)

Step 1: load the data (10 points)

Please use the data called “micro_grades_2015.csv” to answer questions in Part 2. (10 points)

Step 2: Summary statistics (20 points)

Use R to calculate the following summary statistics.

(a)     What are the mean, median, minimum, and maximum score for exam1 for the entire sample? (1 point)

(b)     What is the standard deviation of exam1 for the entire sample? (1 point)

(c)     What are the mean, median, minimum, and maximum score for exam2 for the entire sample? (1 point) (d) What is the standard deviation of exam2 for the entire sample? (1 point)

(e)       What are the mean, median, minimum, and maximum score for finalexam for the entire sample? (1 point)

(f)        What is the standard deviation of finalexam for the entire sample? (1 point)

(g)       Create a histogram for exam1 for the entire sample. Label the figure. (2 points)

(h)       Create a kernel density plot for exam1 for the entire sample. Label the figure. (2 points)

(i)         Create a histogram for exam2 for the entire sample. Label the figure. (2 points)

(j)         Create a kernel density plot for exam2 for the entire sample. Label the figure. (2 points)

(k)       Create a histogram for finalexam for the entire sample. Label the figure. (2 points)

(l)         Create a kernel density plot for finalexam for the entire sample. Label the figure. (2 points)

(m)     Create a scatter plot with exam1 on the horizontal axis and finalexam on the vertical axis. Add a linear trend. Label the figure. (2 points)

Step 3 (25 points)

Now use R to create new variables.

(a)     Create a new variable called overallgrade which takes the average of quiz, exam1, exam2, and finalexam and include it in your data frame.(3 points)

(b)     What are the mean, median, minimum, and maximum of overallgrade. (1 point)

(c)     What are the mean, median, minimum, and maximum of overallgrade for students who scored 80 or more on exam1? (3 points)

(d)     Create a new variable called woverallgrade which takes a weighted average of quiz, exam1, exam2, and finalexam and include it in your data frame. The weights are quiz 10%, exam1 25%, exam2 25%, and finalexam 40%. (3 points)

(e)     What are the mean, median, minimum, and maximum of woverallgrade. (1 point)

(f)      Perform a t-test of whether overallgrade is equal to woverallgrade. According to the t-test, are the two measures of overall grade different in a statistical sense? (3 points)

(g)     Perform a t-test of whether overallgrade is equal to exam1. According to the t-test, could we just use the score on exam 1 to assign an overall grade? (3 points)

(h)     Create a scatter plot with exam1 on the horizontal axis and overallgrade on the vertical axis. Add a linear trend. Label the figure. (3 points)

(i)       Create a new scatter plot with exam1 on the horizontal axis and overallgrade on the vertical axis, but do so only for students who scored 80 or higher on exam1 and exam2. Add a linear trend. Label the figure. (5 points)

Part 4: Knit your file as .docx (5 points)

Knit your file as in docx format. (5 points)